Crystal Structure and Transport Properties of the Homologous

Article pubs.acs.org/IC

Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Crystal Structure and Transport Properties of the Homologous Compounds (PbSe)5(Bi2Se3)3m (m = 2, 3) Selma Sassi,† Christophe Candolfi,† Gael̈ le Delaizir,‡ Sylvie Migot,† Jaafar Ghanbaja,† Christine Gendarme,† Anne Dauscher,† Bernard Malaman,† and Bertrand Lenoir*,† †

Institut Jean Lamour, UMR 7198 CNRS-Université de Lorraine, 2 allée André Guinier-Campus ARTEM, 54011 Nancy, France Sciences des Procédés Céramique et de Traitement de Surface (SPCTS), UMR CNRS 7315-Univsersité de Limoges, Limoges, France

‡

S Supporting Information *

ABSTRACT: We report on a detailed investigation of the crystal structure and transport properties in a broad temperature range (2−723 K) of the homologous compounds (PbSe)5(Bi2Se3)3m for m = 2, 3. Single-crystal X-ray diffraction data indicate that the m = 2, 3 compounds crystallize in the monoclinic space groups C2/m (No. 12) and P21/m (No. 11), respectively. In agreement with diffraction data, highresolution transmission electron microscopy analyses carried out on single crystals show that the three-dimensional crystal structures are built from alternating Pb−Se and m Bi−Se layers stacked along the a axis in both compounds. Scanning electron microcopy and electron-probe microanalyses reveal deviations from the nominal stoichiometry, suggesting a domain of existence in the pseudo binary phase diagram at 873 K. The complex atomic-scale structures of these compounds lead to very low lattice thermal conductivities κL that approach the glassy limit at high temperatures. A comparison of the κL values across this series unveiled an unexpected increase with increasing m from m = 1 to m = 3, in contrast to the expectation that increasing the structural complexity should tend to lower the thermal transport. This result points to a decisive role played by the Pb−Se/Bi− Se interfaces in limiting κL in this series. Both compounds behave as heavily doped n-type semiconductors with relatively low electrical resistivity and thermopower values. As a result, moderate peak ZT values of 0.25 and 0.20 at 700 K were achieved in the m = 2, 3 compounds, respectively. The inherent poor ability of these structures to conduct heat suggests that these homologous compounds may show interesting thermoelectric properties when properly optimized by extrinsic dopants.

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INTRODUCTION Thermoelectric materials that enable solid-state conversion of heat into electricity and vice versa can be used in applications related to waste-heat recovery, power generation, or cooling of electronic devices or small systems.1−3 So far, the widespread use of this technology has been hampered by the low efficiency of thermoelectric materials, which is governed by their dimensionless figure of merit ZT defined as ZT = α2T/ρκ.1−3 Achieving high efficiency at a given absolute temperature T requires an unusual combination of high thermopower α, low electrical resistivity ρ, and low total thermal conductivity κ. The challenge in designing an ideal thermoelectric material thus lies in efficiently scattering acoustic phonons without causing a concomitant strong reduction in the charge carrier mobility. Materials exhibiting simultaneously high mobility and low lattice thermal conductivity are usually referred to as “phonon glass, electron crystal” (PGEC) in the literature.4,5 Materials crystallizing in a complex unit cell provide a possible route to finding novel efficient thermoelectric materials. Their structural complexity gives rise to extremely low lattice thermal conductivity κL, the temperature depend© XXXX American Chemical Society

ence of which often mirrors that of glassy compounds. In addition to Zintl phases, clathrates, or cluster compounds,6−20 complex crystal structures also prevail in homologous compounds. 21,22 Their crystal structure is formed by fundamental building blocks that expand along one or several dimensions by regular increments. The structural complexity can be easily manipulated by varying the number of building blocks which, in turn, offers a tuning parameter of the physical properties. Examples of naturally occurring homologous series are found in sulfosalt minerals such as the lillianite and pavonite series of general chemical formula Mn+1BiSn+5 (M = Ag/Bi, Cu/ Bi; n ≥ 2) and Pbn−1−2xBi2+xAgxSn+2, respectively, with n being either integer or noninteger.23,24 Recent investigations on the synthetic lillianites Pb7Bi4Se13 and Pb6Bi2Se9, both belonging to the series of general formula PbN−1Bi2SeN+2 with N = 4.5, 7, respectively, have demonstrated their potential as thermoelectric materials.25,26 These compounds are narrow-band gap n-type semiconductors and, remarkably, exhibit very low lattice Received: October 16, 2017

A

DOI: 10.1021/acs.inorgchem.7b02656 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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thermal conductivity (∼0.3 and ∼0.9 W m−1 K−1 at 300 K for Pb7Bi4Se13 and Pb6Bi2Se9, respectively) resulting in a peak ZT value of 0.9 at 775 K in Pb7Bi4Se13.25 The minerals called cannizzarites are naturally occurring Pb− Bi sulfosalts that provide another interesting example of a homologous series.27−33 The crystal structure is composed of pseudotetragonal layers (Q) that alternate with a doubleoctahedron layer (H) of pseudohexagonal symmetry. The general formulas of these layers can be written as M2S2 and M4S6, respectively, where M is Pb/Bi. When m H layers match n Q layers, the structure is referred to as semicommensurate and then corresponds to a variable-fit homologous series written as mH:nQ.31−33 Various H:Q matches have been predicted and evidenced experimentally in minerals with, among others, the shortest possible type 3H:5Q that leads to the chemical formula Pb5Bi6S14.33 The selenide counterpart of this last compound belongs to the subseries (PbSe)5(Bi2Se3)3m (m = 1−4), which has recently attracted attention for its interesting physical properties.34−39 Their crystal structure consists of an alternate stacking of Pb− Se layers separated by m Bi−Se layers interacting via van der Waals gaps. This multilayer heterostructure formed by a topological insulator (Bi2Se3) and an ordinary insulator (PbSe) harbors nontrivial topological states for m = 2.40−42 The intercalation of Cu into the van der Waals gap between the two Bi2Se3 adjacent layers results in bulk superconductivity at 2.9 K, making this system an interesting platform for the search of topological superconductivity.42 Bulk superconductivity was also observed in the m = 1 compound upon inserting Ag atoms that were shown to dope both the Pb−Se and Bi−Se layers by atom probe tomography.41,43 Investigations of the thermoelectric properties of the m = 1 compound evidenced a peak ZT of 0.5 at 723 K arising from a combination of n-type semiconducting-like electrical properties and very low κL values.37,38 Although the crystal structures and some physical properties of the m = 1, 2, 4 compounds have been reported,34−39 the thermoelectric properties of the stable m = 2, 3 members (the m = 4 member is metastable) have not been explored in detail so far. In addition, a full determination of the space group and atomic coordinates of the m = 3 compound is still lacking. Here, we report on the synthesis, crystal structure determination, and transport property measurements in a broad range of temperatures (2−700 K) of the m = 2, 3 compounds of this series. A combination of single-crystal X-ray diffraction, highresolution transmission electron microscopy (HRTEM), and scanning electron microscopy in high-angle annular dark-field mode (STEM-HAADF) was used to provide a precise description of the crystal structure by direct observation of the alternating layers at an atomic scale. In order to determine general trends in the crystal structure and transport properties with varying m, we further characterized the crystal structure and some basic physical parameters of the m = 1 compound. Our results show that m = 2, 3 compounds both behave as degenerate n-type semiconductors. Intriguingly, despite an increase in the structural complexity with increasing m, the lattice thermal conductivity increases concomitantly, suggesting that the interfaces between both types of layers play a decisive role in the thermal transport. These two main characteristics yield moderate ZT values that reach ∼0.25 and 0.20 at 700 K in the m = 2, 3 compounds, respectively.

Article

EXPERIMENTAL SECTION

Syntheses. All manipulations were carried out in an argon-filled, dry glovebox. Polycrystalline samples of the target compositions Pb5Bi12Se23 (m = 2) and Pb5Bi18Se32 (m = 3) were synthesized by a two-step process. In a first step, the two precursors PbSe and Bi2Se3 were prepared by direct reaction of stoichiometric quantities of highpurity powders of Pb (99.999%), Bi (99.999%), and Se (99.999%). The mixtures were placed in evacuated quartz tubes sealed under secondary vacuum, heated to 1393 K in a rocking furnace, held at this temperature for 12 h, and finally cooled to room temperature over 2 h. In a second step and after verification of the phase purity of each precursor by laboratory powder X-ray diffraction, appropriate stoichiometric ratios of PbSe and Bi2Se3 were ground into fine powders, pelletized, and loaded into evacuated quartz tubes sealed under secondary vacuum. The pellets were annealed for 10 days at 873 K: that is, below the peritectic decomposition temperatures of 973 and 993 K for the m = 2, 3 phases, respectively, according to the pseudo binary phase diagram PbSe−Bi2Se3 determined by Zemskov et al.36 After the tubes were quenched in room-temperature water, the pellets were reground into fine powders and consolidated in a graphite die by spark plasma sintering at 673 K for 10 min under a pressure of 80 MPa. The experimental densities of the two samples, determined by geometrical dimensions and weight, were above 97% of the theoretical density. Powder X-ray Diffraction. The crystal structure and phase purity of the precursors and of the final compounds were verified by powder X-ray diffraction (PXRD). These measurements were performed at 300 K using a D8 Bruker Advance diffractometer equipped with a LynxEye detector (Cu Kα1 radiation, λ = 1.54056 Å). Single Crystal X-ray Diffraction and Structure Determination. Single crystals grown on the surface of the pellets during the annealing treatment could be isolated and employed for crystal structure determinations. The single crystals of needlelike shape (Figure S1 in the Supporting Information) were glued on the tip of a quartz fiber and mounted on a goniometer head. Data acquisition was performed at 300 K using a Bruker APEX-II diffractometer equipped with a CCD detector using Mo Kα radiation (λ = 0.71073 Å). The structure solution was obtained by direct methods and refined by fullmatrix least-squares techniques with the Sir97 and SHELX-2013 software, respectively, implemented through the WinGX suite.44 In agreement with prior studies,34−37 the intensity data collected for the m = 2 compound were best indexed in the monoclinic space group C2/m. The crystal structure of the m = 3 compound has been successfully solved in the monoclinic space group P21/m. Possible mixed Pb/Bi occupancies on several Pb crystallographic sites have been suggested in Pb5Bi6Se14 on the basis of resonant scattering at high-energy K-edge experiments.45 Despite the possibility of similar disorder in the m = 2, 3 compounds, the similar atomic scattering factors of Pb and Bi (Z = 82 and 83, respectively) did not allow us to consider mixed occupancies in our refinements. We further tried to discriminate the Pb from the Bi atoms by considering bond strength− bond length relationships among Pb2+, Bi3+, and Se2− ions using the VALENCE software, which is based on the bond valence model.46,47 The results obtained within this model tend to indicate that the atoms located in the distorted octahedra (atomic positions labeled Pb1 and Pb2 in the following) exhibit an ∼3+ valence state, suggesting that these atoms are in fact mostly Bi atoms. The other atoms in this layer, located in square-based-pyramidal polyhedra, are found to exhibit an ∼2+ valence state consistent with the presence of only Pb atoms. The Pb−Se and Bi−Se distances calculated considering these valence states are in agreement with the refined bond lengths. The two remaining Pb atoms would be then distributed over the 6, 12, and 18 Bi positions in the m = 1−3 compounds, respectively. The analysis of the Bi−Se interatomic distances does not allow further determination of whether Pb preferentially occupies specific positions. It should be kept in mind that this attempt at discriminating both atoms relies on the values used in the valence bond model for the measurement of the size of the two ions involved in the bonding: that is, Pb2+−Se2− and Bi3+−Se2−. This tentative assignment should therefore be taken with some caution. B


Article

Inorganic Chemistry Nevertheless, it can be noted that, according to the ionic radii of the Pb2+, Bi3+, and Se2− ions, that is, 1.17, 1.33, and 1.84 Å, respectively,48 the interatomic distances given in Table 4 and Tables S5−S7 in the Supporting Information are in fair agreement with these aforementioned hypotheses. In the absence of an unambiguous model for the mixed occupancies, we will consider in the following a structural model where the Pb and Bi atoms occupy distinct layers in agreement with the description of the crystal structure used in the literature.34−42 The relevant information on data collection and refinements for these two compounds are summarized in Table 1. The atomic coordinates and

Table 2. Atomic Coordinates and Equivalent Isotropic Displacement Parameters (Å2) for the m = 3 Compounda

Table 1. Selected Crystal Data and Structure Refinement Details of the (PbSe)5(Bi2Se3)3m phases for m = 2, 3 molar mass (g mol−1) symmetry space group a (Å) b (Å) c (Å) β (deg) V (Å3) Z ρcalcd (g cm−3) 2θ range (deg) radiation (Å) abs coeff (mm−1) index range

no. of data/restraints/params R indices (Fo > 4σ(Fo)) goodness of fit on F2

Pb5Bi12Se23

Pb5Bi18Se32

5360.07 monoclinic C2/m 53.168(4) 4.1786(3) 21.550(2) 107.491(3) 4566.4(6) 4 7.79 1.60−60.63 Mo Kα; λ = 0.71073 82.74 −73 ≤ h ≤ 74 −5 ≤ k ≤ 5 −30 ≤ l ≤ 30 7688/0/242 R1 = 0.066 wR2 (all) = 0.2339 0.963

7324.68 monoclinic P21/m 35.667(2) 4.1670(2) 21.530(1) 102.275(2) 3126.7(1) 2 7.78 1.64−50.05 Mo Kα; λ = 0.71073 82.48 −25 ≤ h ≤ 25 −4 ≤ k ≤ 4 −42 ≤ l ≤ 42 6356/0/386 R1 = 0.060 wR2 (all) = 0.2151 1.028

isotropic displacement parameters for all atoms are given in Table 2 for the m = 3 compound (for comparison, the crystallographic parameters determined for the m = 1, 2 compounds are given in Tables S1−S4 in the Supporting Information). The anisotropic thermal displacement parameters are given in Table 3. The Pb−Se interatomic distances are gathered in Table 4 for all of the three compounds for comparison purposes, while the Bi−Se interatomic distances are provided in Tables S5−S7. Scanning Electron Microscopy (SEM). SEM experiments were performed on polished bulk pieces cut from the consolidated ingots using a Quanta FEG 650 (FEI) with energy-dispersive X-ray (EDX) microanalysis. Backscattered electron (BSE) images and elemental Xray maps were taken to assess phase purity and determine the spatial distribution of Pb, Bi, and Se. Electron Probe Microanalysis (EPMA). Bulk pieces of the consolidated samples were carefully polished using alumina powders. The chemical composition of each specimen was examined by EPMA using a JEOL JXA 8530F instrument equipped with wavelengthdispersive spectrometers. PbTe, elemental Bi, and SnSe were used as standards to determine the Pb, Bi, and Se concentrations, respectively. The chemical formulas were normalized to 40 and 55 atoms per chemical formula for the m = 2, 3 compounds, respectively. Transmission Electron Microscopy (TEM). Thin slices were prepared from the single crystals perpendicular to the growth direction (which corresponds to the b axis of the crystal structure) by the dual focused ion beam (FIB)−scanning electron microscope system using the in situ lift-out technique. Scanning TEM (STEM) in high-angle annular dark-field (HAADF) mode, annular bright-field (ABF), and high-resolution TEM (HRTEM) were performed with a JEOL ARM 200F−cold FEG TEM/STEM microscope operating at 200 keV and equipped with a spherical aberration (Cs) probe and image correctors.

atom

x

y

z

Ueq

Pb1 Pb2 Pb3 Pb4 Pb5 Bi1 Bi2 Bi3 Bi4 Bi5 Bi6 Bi7 Bi8 Bi9 Bi10 Bi11 Bi12 Bi13 Bi14 Bi15 Bi16 Bi17 Bi18 Se1 Se2 Se3 Se4 Se5 Se6 Se7 Se8 Se9 Se10 Se11 Se12 Se13 Se14 Se15 Se16 Se17 Se18 Se19 Se20 Se21 Se22 Se23 Se24 Se25 Se26 Se27 Se28 Se29 Se30 Se31 Se32

0.46557(4) 0.53820(4) 0.55452(4) 0.55342(4) 0.55116(5) 0.94543(4) 0.94450(4) 0.78526(4) 0.67284(4) 0.78313(4) 0.78353(4) 0.94521(4) 0.94472(4) 0.67444(4) 0.94524(4) 0.67253(4) 0.78131(4) 0.94467(4) 0.67235(4) 0.78437(4) 0.78171(4) 0.66988(4) 0.67671(4) 0.82758(10) 0.82748(10) 0.82566(10) 0.82884(10) 0.90078(10) 0.89972(10) 0.82596(10) 0.90051(10) 0.82900(10) 0.89993(10) 0.90001(10) 0.72514(10) 0.90056(10) 0.00026(10) 0.72431(9) 0.72745(9) 0.72504(9) 0.00064(8) 0.62962(9) 0.72785(9) 0.62926(9) 0.62586(9) 0.72978(9) 0.99969(8) 0.62669(9) 0.62726(9) 0.54111(9) 0.62495(10) 0.54429(9) 0.53043(10) 0.47160(9) 0.46990(9)

1/4 3/4 3/4 3/4 3/4 1/4 3/4 3/4 3/4 3/4 1/4 3/4 1/4 1/4 3/4 3/4 1/4 1/4 1/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 3/4 1/4 3/4 1/4 1/4 3/4 3/4 1/4 1/4 1/4 3/4 3/4 1/4 3/4 3/4 3/4 1/4 1/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 1/4 3/4 3/4

0.33733(6) 0.06768(7) 0.47393(7) 0.26733(7) 0.86364(8) 0.67609(6) 0.17447(6) 0.45390(6) 0.96965(6) 0.11822(6) 0.62002(6) 0.50900(6) 0.34155(6) 0.47056(6) 0.84246(6) 0.63456(6) −0.95090(6) 0.00825(6) 0.13808(6) 0.28614(6) 0.78484(6) 0.80120(6) 0.30510(6) 0.18803(16) 0.69205(16) 0.85612(16) 0.35695(16) 0.60524(16) 0.10295(16) 0.02101(16) 0.43814(16) 0.52610(16) 0.27032(16) 0.93674(16) 0.04404(15) 0.77122(16) 0.58365(13) 0.87566(15) 0.21092(12) 0.70877(15) 0.75073(13) 0.39928(15) 0.54454(15) 0.23754(16) 0.89716(16) 0.37853(15) 0.08286(13) 0.55883(16) 0.06759(16) 0.96761(15) 0.72916(14) 0.36649(14) 0.15859(16) 0.43678(15) 0.24254(15)

0.0194(3) 0.0217(3) 0.0259(3) 0.0281(3) 0.0367(4) 0.0102(3) 0.0103(3) 0.0100(2) 0.0128(3) 0.0110(3) 0.0106(3) 0.0094(4) 0.0098(4) 0.0109(3) 0.0087(4) 0.0120(3) 0.0110(3) 0.0099(3) 0.0125(3) 0.0098(3) 0.0112(3) 0.0125(3) 0.0107(3) 0.0107(7) 0.0108(7) 0.0106(6) 0.0092(7) 0.0088(7) 0.0099(6) 0.0101(6) 0.0080(8) 0.0096(8) 0.0091(6) 0.0113(6) 0.0089(6) 0.0103(7) 0.0087(6) 0.0099(7) 0.0090(6) 0.0097(6) 0.0085(7) 0.0079(7) 0.0075(6) 0.0130(6) 0.0113(6) 0.0083(7) 0.0069(7) 0.0115(6) 0.0128(6) 0.0142(6) 0.0143(7) 0.0104(6) 0.0185(7) 0.0122(6) 0.0130(6)

a

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. C


Article

Inorganic Chemistry Table 3. Anisotropic Thermal Displacement Parameters (Å2) for the m = 3 Compound at 300 Ka

a

atom

U11

U22

U33

U13

Pb1 Pb2 Pb3 Pb4 Pb5 Bi1 Bi2 Bi3 Bi4 Bi5 Bi6 Bi7 Bi8 Bi9 Bi10 Bi11 Bi12 Bi13 Bi14 Bi15 Bi16 Bi17 Bi18 Se1 Se2 Se3 Se4 Se5 Se6 Se7 Se8 Se9 Se10 Se11 Se12 Se13 Se14 Se15 Se16 Se17 Se18 Se19 Se20 Se21 Se22 Se23 Se24 Se25 Se26 Se27 Se28 Se29 Se30 Se31 Se32

0.0180(5) 0.0200(6) 0.0349(7) 0.0341(7) 0.0387(8) 0.0126(5) 0.0130(5) 0.0117(5) 0.0152(5) 0.0130(5) 0.0127(5) 0.0127(5) 0.0117(5) 0.0126(5) 0.0133(5) 0.0158(5) 0.0136(5) 0.0133(5) 0.0168(5) 0.0118(5) 0.0138(5) 0.0167(5) 0.0131(5) 0.0059(2) 0.0093(3) 0.0067(3) 0.0061(2) 0.0084(3) 0.0062(2) 0.0090(3) 0.0059(2) 0.0055(2) 0.0055(2) 0.0091(3) 0.0089(3) 0.0065(3) 0.0076(3) 0.0117(3) 0.0087(3) 0.0105(3) 0.0086(4) 0.0064(2) 0.0076(2) 0.0096(3) 0.0091(3) 0.0085(3) 0.0077(3) 0.0117(3) 0.0098(3) 0.0163(4) 0.0083(3) 0.0139(4) 0.0296(6) 0.0156(3) 0.0179(4)

0.0191(7) 0.0213(7) 0.0195(8) 0.0254(8) 0.0322(9) 0.0103(9) 0.0105(7) 0.0110(6) 0.0135(6) 0.0131(6) 0.0120(7) 0.0082(9) 0.0105(9) 0.0122(6) 0.0053(1) 0.0113(7) 0.0122(6) 0.0093(9) 0.0114(8) 0.0107(7) 0.0123(6) 0.0119(7) 0.0118(7) 0.0164(1) 0.0137(9) 0.0159(7) 0.0116(1) 0.0095(1) 0.0146(7) 0.0093(8) 0.0091(2) 0.0128(3) 0.0117(8) 0.0151(8) 0.0112(8) 0.0148(9) 0.0142(8) 0.0116(1) 0.0121(8) 0.0112(8) 0.0119(1) 0.0116(9) 0.0080(8) 0.0179(8) 0.0129(7) 0.0101(8) 0.0077(8) 0.0133(6) 0.0145(7) 0.0139(7) 0.0182(8) 0.0069(7) 0.0136(9) 0.0096(7) 0.0120(7)

0.0207(6) 0.0233(6) 0.0241(6) 0.0266(6) 0.0370(8) 0.0082(5) 0.0078(5) 0.0074(5) 0.0103(5) 0.0074(5) 0.0071(5) 0.0075(5) 0.0074(5) 0.0082(5) 0.0081(5) 0.0090(5) 0.0078(5) 0.0079(5) 0.0097(5) 0.0074(5) 0.0077(5) 0.0094(5) 0.0075(5) 0.0094(3) 0.0090(3) 0.0088(3) 0.0098(3) 0.0085(3) 0.0088(3) 0.0121(3) 0.0098(4) 0.0095(3) 0.0099(3) 0.0099(4) 0.0069(3) 0.0096(3) 0.0042(2) 0.0065(3) 0.0070(3) 0.0072(3) 0.0056(3) 0.0059(2) 0.0066(3) 0.0113(3) 0.0129(3) 0.0066(3) 0.0047(2) 0.0109(3) 0.0147(4) 0.0130(4) 0.0154(4) 0.0097(4) 0.0099(4) 0.0130(3) 0.0084(3)

0.0034(1) 0.0035(2) 0.0080(4) 0.0105(4) 0.0027(7) 0.0031(5) 0.0033(1) 0.0022(1) 0.0036(2) 0.0030(1) 0.0023(3) 0.0026(5) 0.0027(1) 0.0031(7) 0.0029(8) 0.0027(6) 0.0033(8) 0.0037(9) 0.0034(2) 0.0031(2) 0.0027(5) 0.0038(3) 0.0026(6) 0.0010(4) 0.0011(6) 0.0006(1) 0.0015(9) 0.0019(2) 0.0014(8) 0.0024(5) 0.0031(5) −0.0011(1) 0.0008(1) 0.0023(8) 0.0024(9) 0.0016(1) 0.0011(1) 0.0017(5) 0.0029(6) 0.0014(2) 0.0024(9) 0.0015(3) 0.0003(1) 0.0020(3) 0.0042(7) 0.0024(2) −0.0001(4) 0.0049(2) 0.0039(5) 0.0043(7) 0.0002(7) 0.0009(5) −0.0007(8) 0.0066(8) 0.0010(2)

reflectance spectroscopy on a Thermo Scientific Nicolet 6700 FTIR spectrophotometer equipped with an integrated sphere. Raw reflectance data R were used to estimate the absorption coefficient using the Kubelka−Munk relation F(R) = (1 − R)2/2R.49 The data were then plotted as (F(R)ℏω)n versus ℏω, where ℏω is the incoming photon energy, to estimate the transition onset energies corresponding to the optical band gap Eg. In the absence of electronic band structure calculations, both direct (n = 2) and indirect (n = 1/2) extrapolations of the absorption edge to zero were considered. Transport Property Measurements. Due to the layered crystal structure of the samples, the transport properties were measured on samples cut perpendicular and parallel to the pressing direction in the appropriate shape and size with a diamond-wire saw. Electrical resistivity, thermopower, and thermal conductivity were measured simultaneously on bar-shaped samples (typical dimensions 2 × 2 × 8 mm3) between 5 and 300 K using the thermal transport option of a physical property measurement system (PPMS, Quantum Design). Good electrical and thermal contacts were ensured by gluing copper bars using conductive silver epoxy. Hall effect measurements were performed on the same samples using a five-probe configuration and the AC transport option of the PPMS. The five copper wires were brazed onto the samples using a low-melting-point braze. The transverse electrical resistivity ρxy was measured between 5 and 300 K under magnetic fields μ0H ranging between −1 and +1 T. Possible magnetoresistive contributions were dismissed by considering the antisymmetric part of ρxy under magnetic field reversal following the formula [ρxy(+μ0H) − ρxy(−μ0H)]/2. The Hall electron concentrations nH and mobilities μH were inferred by the single-band formulas nH = −1/RHe and μH = RH/ρ, where RH is the Hall coefficient and e is the elementary charge. The experimental uncertainty associated with the low-temperature measurements of the electrical resistivity, thermopower, thermal conductivity, and Hall coefficient are estimated to be 5% for each. Electrical resistivity and thermopower were measured simultaneously on bar-shaped samples (typical dimensions 1.5 × 1.5 × 7 mm3) between 300 and 700 K under a low-pressure helium atmosphere using a ZEM-3 setup (Ulvac-Riko). The thermal conductivity was determined between 300 and 700 K by combining thermal diffusivity a and specific heat Cp measurements according to the relation κ = aCpd, where d is the experimental density. Thermal diffusivity was measured on graphite-coated disk-shaped (perpendicular direction, 10 mm in diameter and 1 mm in thickness) and prismshaped (parallel direction, 6 × 6 × 1 mm3) samples by a laser flash technique using an LFA 427 instrument (Netzsch). Specific heat was approximated by the Dulong−Petit law, while the temperature dependence of the density has been neglected in the present case. The experimental uncertainties in the measurements of the electrical resistivity, thermopower, and thermal conductivity are estimated to be 5%, 5%, and 10%, respectively. The combined experimental uncertainty in the ZT values is estimated to be 17%.50

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RESULTS AND DISCUSSION Crystal Structure. On the basis of the single-crystal X-ray diffraction data, both compounds crystallize in a monoclinic structure with space group C2/m for m = 2 and P21/m for m = 3 (Table 1). The lattice parameters a, b, and c and monoclinic angle β obtained for the m = 2 compound are in good agreement with prior diffraction studies.34−37 The phase purity of the single crystals used for structural characterizations was confirmed by X-ray diffraction performed on ground crystals (not shown). The PXRD results further revealed that single crystals of both the m = 2 and m = 3 compounds grew simultaneously on the surface of the polycrystalline ingot of the m = 3 compound. Surprisingly, a large majority of these single crystals were found to correspond to the m = 2 phase. Some crystals of the m = 3 compound could nevertheless be isolated. Figure 1 shows a representation of the crystal structure of the three compounds projected along the b axis. The structure is

By symmetry, U23 and U12 are both equal to zero for all atoms.

Absorption Spectroscopy. Optical measurements were carried out at room temperature on powdered samples using diffuse D


Article

Inorganic Chemistry

Table 4. Comparison of the Interatomic Distances (d < 4 Å) for the Pb Atoms in the Series (PbSe)5(Bi2Se3)3m (m = 1, 2 and 3) at 300 Ka Pb5Bi6Se14

Pb5Bi18Se32b

Pb5Bi12Se23

bond type

distance

bond type

distance

bond type

distance

Pb1−Se Pb1−Se (×2) Pb1−Se (×2) Pb1−Se mean value Pb2−Se Pb2−Se (×2) Pb2−Se (×2) Pb2−Se mean value Pb3−Se Pb3−Se (×2) Pb3−Se (×2) Pb3−Se Pb3−Se (×2) mean value Pb4−Se Pb4−Se (×2) Pb4−Se (×2) Pb4−Se Pb4−Se (×2) mean value Pb5−Se Pb5−Se (×2) Pb5−Se (×2) Pb5−Se (×2) mean value

2.760(5) 2.936(4) 2.974(4) 3.215(6) 2.966 2.806(6) 2.921(4) 3.008(4) 3.116(5) 2.963 2.935(6) 3.085(4) 3.133(4) 3.417(4) 3.445(3) 3.074 2.908(6) 3.054(4) 3.135(4) 3.508(4) 3.555(4) 3.057 2.910(5) 3.059(4) 3.148(4) 3.337(5) 3.065

Pb1−Se Pb1−Se (×2) Pb1−Se (×2) Pb1−Se mean value Pb2−Se Pb2−Se (×2) Pb2−Se (×2) Pb2−Se mean value Pb3−Se Pb3−Se (×2) Pb3−Se (×2) Pb3−Se Pb3−Se (×2) mean value Pb4−Se Pb4−Se (×2) Pb4−Se (×2) Pb4−Se Pb4−Se (×2) mean value Pb5−Se Pb5−Se (×2) Pb5−Se (×2) Pb5−Se (×2) mean value

2.743(4) 2.957(3) 2.959(2) 3.242(4) 2.969 2.776(4) 2.921(3) 3.014(3) 3.171(3) 2.969 2.905(4) 3.084(2) 3.116(3) 3.407(3) 3.497(3) 3.061 2.911(4) 3.052(3) 3.115(2) 3.498(3) 3.587(2) 3.049 2.869(4) 3.063(2) 3.147(3) 3.343(3) 3.057

Pb1−Se29 Pb1−Se32 (×2) Pb1−Se31 (×2) Pb1−Se28 mean value Pb2−Se27 Pb2−Se30 (×2) Pb2−Se27 (×2) Pb2−Se26 mean value Pb3−Se31 Pb3−Se29 (×2) Pb3−Se31 (×2) Pb3−Se19 Pb3−Se25 (×2) mean value Pb4−Se32 Pb4−Se29 (×2) Pb4−Se30 (×2) Pb4−Se19 Pb4−Se21 (×2) mean value Pb5−Se30 Pb5−Se32 (×2) Pb5−Se27 (×2) Pb5−Se22 (×2) mean value

2.742(3) 2.943(2) 2.962(2) 3.241(3) 2.960 2.768(3) 2.911(2) 3.014(2) 3.177(3) 2.960 2.895(4) 3.076(2) 3.109(3) 3.404(3) 3.508(3) 3.050 2.912(3) 3.050(2) 3.111(2) 3.489(3) 3.578(3) 3.050 2.847(3) 3.066(2) 3.133(2) 3.338(3) 3.049

a

The indices of the Pbi atoms correspond to the indices used in the atomic coordinate tables. The mean value of the interatomic distances is also given for the octahedral and square-based pyramidal environments of the five atoms to underline that both Pb1 and Pb2 show distances that are in agreement with an ∼3+ valence state according to the valence bond model,47 suggesting that both sites might be mostly occupied by Bi atoms. bThe indices of the Sei atoms are referenced according to Figure 2.

Figure 1. Crystal structure of Pb5Bi6Se14 (m = 1), Pb5Bi12Se23 (m = 2) and Pb5Bi18Se32 (m = 3) projected along the b axis showing alternating Pb−Se and Bi−Se structural units. The Pb atoms are shown in dark gray, the Bi atoms in purple, and the Se atoms in green. The unit cell for each compound is represented by the blue parallelepiped. Note that, in monoclinic crystal structures, the choice in the definition of the a and c axes is free so that both axes can be interchanged. In such a case, the x and z coordinates of all atoms should be interchanged as well.

atoms (Figure 2). These octahedra share faces to form a twooctahedra-thick, slightly modulated ribbon that runs along the c axis of the crystal structures. Regardless of m, the structure contains five crystallographically independent Pb atoms. Both Pb1 and Pb2 are located at the center of a distorted octahedron. Pb3 and Pb4 atoms occupy an 8-fold coordinated position with tricapped-square-based-pyramidal geometry, while the Pb5 atoms show a 7-fold coordination environment with bicapped-square-based-pyramidal geometry (see Figure 2). The Pb and Bi atoms in the m = 2, 3 compounds show

divided into two alternating structural units made of PbSe-type and Bi2Se3-type layers, with the number of Bi−Se layers specified by the integer m. The Pb−Se layers correspond to two layers cut perpendicularly to the [100] direction of the fcc lattice of PbSe. The Bi−Se layers correspond to five-layer slabs (that is, one quintet) that build the crystal structure of Bi2Se3. These two structural units interact via weak Pb/Bi−Se bonds. The misfit between these two types of layers gives rise to strong lattice distortion near the boundaries. Within the Bi−Se layers, Bi atoms show distorted-octahedral environments formed by Se E


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Figure 2. Coordination polyhedral of Pb and Bi atoms in the m = 3 compound. The chemical environments of these atoms in the m = 1, 2 compounds are similar.

Figure 3. HAADF-STEM images of the m = 1 (upper left panel), m = 2 (upper middle panel), and m = 3 (right upper panel) single crystals. All of these images were taken along the [010] zone axis. An overlaid crystal structure is shown in each panel (Pb atoms in green, Bi atoms in pink, and Se atoms in yellow). The lower panels show the corresponding electron diffraction patterns.

skutterudites.51−53 This first characteristic is not confined to this series and has already been observed in several other Pbcontaining sulfide and selenide structures.25,26,31−33 The second characteristic is tied to the chemical environment of the Pb and Bi atoms. All of the Pb atoms show a distorted environment with short Pb−Se bonds and elongated Pb−Se bonds along the long axis of the polyhedra (Table 4 and Figure 2). Similarly, the Bi atoms exhibit a slightly distorted octahedral environment with systematically three short Bi−Se distances of ∼2.85 Å and three longer distances of ∼3.08 Å (see Tables S5−S7 in the Supporting Information). This strong asymmetric environment is likely the result of the stereoactivity of the Pb2+ and Bi3+ lonepair electrons.54,55 Similar distortions attributed to stereoactive lone-pair electrons were also observed in the ternaries Pb7Bi4Se13 and Pb6Bi2Se9 and in the monoclinic compound K2Bi8Se13, for instance.25,26,56 Transmission Electron Microscopy on Single Crystals. For a more detailed structural characterization, high-resolution

similar polyhedral environments with varying degrees of distortion (Table 4 and Tables S5−S7 in the Supporting Information). In the m = 2 compound, the two Bi−Se ribbons are connected by Se−Se bonds with distances varying between 3.436(4) and 3.550(4) Å, reflecting a slight modulation of the ribbons. In the m = 3 compound, the Bi2Se3 layer intercalated between the two other adjacent Bi2Se3 layers (see Figure 1) is formed by two rows of Bi−Se octahedra, which are shifted from each other along the c axis. The insertion of this third layer slightly modifies the Se−Se distances observed in the m = 2 compound, resulting in distances varying between 3.447(2) and 3.546(2) Å. The results further reveal two important characteristics in the present series of compounds which are nearly insensitive to the value of m. First, the Pb atoms exhibit the highest thermal displacement parameters (Tables 2 and 3 and Tables S1−S4 in the Supporting Information), with values similar to those typically observed in cage compounds such as clathrates and F


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Inorganic Chemistry transmission electron spectroscopy was used to examine the asgrown single crystals of the m = 2, 3 compounds. For comparison purposes, single crystals of the m = 1 compound have been also studied. Figure 3 shows the HAADF-STEM images of the m = 1−3 compounds taken along the [010] zone axis. The corresponding electron diffraction patterns along this axis are also shown. All of the diffraction patterns are consistent with the monoclinic crystal structure of these compounds and can be well indexed with the P21/m (m = 1, 3) and C2/m (m = 2) space groups. Both the lattice parameters and monoclinic distortion angles determined from these patterns are consistent with those refined by single-crystal X-ray diffraction. The highresolution STEM images agree with the X-ray diffraction data and show the presence of alternating Pb−Se and m Bi−Se structural units. In these images, only the Pb and Bi atoms are visible due to the brightness of the atomic layers, which are proportional to Zn (where Z is the element number of the atom and 1 < n < 2).57 The similar Z numbers of Pb and Bi did not enable us to further distinguish possible mixed occupancies on the Pb and Bi sites. The Se atoms were visualized by collecting annular bright-field (ABF) images (Figure S2 in the Supporting Information). No additional modulation of the crystal structure, arising from charge-density waves, additional atomic occupations, or insertion between the layers or stacking faults, is observed in the diffraction patterns corresponding to these images. Line profiles (not shown), taken perpendicular and parallel to the layers, did not provide any clear experimental evidence of the presence of vacancies on the Pb, Bi, or Se sites in these single crystals in agreement with our X-ray diffraction data. Phase Purity and Chemical Homogeneity of Polycrystalline Specimens. We next turn to the characterizations of the polycrystalline specimens of the m = 2, 3 compounds. The PXRD patterns (Figure 4) collected on both samples are consistent with the theoretical patterns inferred from the singlecrystal X-ray data, suggesting the absence of secondary phases within the detection limits of PXRD. Of note, the anisotropic crystal structure of these compounds leads to a strong renormalization of the intensities of the diffraction peaks with the h00 reflections (equivalent to 00l reflections in the present case) appearing as the most intense peaks in the m = 2, 3 compounds. This preferential orientation did not allow further analyses of these patterns by Rietveld refinements. SEM analyses performed on both pressed samples (Figure 5) revealed a more complex situation. While the elemental X-ray maps reveal a uniform distribution of Se, some slight but discernible spatial fluctuations in the Pb and Bi concentrations can be observed in these images with Pb-rich (Bi-poor) and Pbpoor (Bi-rich) zones (see Figure 5). This slight inhomogeneous distribution suggests a possible domain of existence at 873 K for each compound or an exsolution process similar to that observed in tetrahedrites, for instance.58−61 EPMA measurements corroborate this observation and show that the distribution of Pb and Bi corresponds to two phases with close chemical compositions. The average compositions are Pb 4 . 6 4 Bi 1 2 . 3 5 Se 2 3 . 2 0 and Pb 6 . 5 6 Bi 1 0 . 6 8 Se 2 3 . 2 0 and are Pb4.04Bi18.32Se32.52 and Pb5.71Bi17.13Se32.52 for the m = 2, 3 compounds, respectively. The absence of clear peak splitting or peak broadening in the PXRD patterns suggests that these phases exhibit very similar lattice parameters, which is consistent with their close chemical compositions and with the similar ionic radii of Pb2+ and Bi3+. Of note, in both compounds, the sum of the Pb and Bi concentrations is found

Figure 4. Powder X-ray diffraction patterns of the polycrystalline (a) m = 2 and (b) m = 3 compounds synthesized from the PbSe and Bi2Se3 precursors. The positions of the Bragg reflections, as calculated from single-crystal X-ray diffraction data, are marked by green vertical ticks. For each compound, the main reflections have been indexed.

to be close to the expected value (that is, 17 and 23 for the m = 2, 3 compounds, respectively) to within experimental uncertainty. Optical Measurements. Figure 6 shows the optical absorption spectra collected on the m = 2, 3 compounds assuming direct transitions (see Figure S3 in the Supporting Information for indirect transitions). For comparison, data collected on the m = 1 sample are also shown. The spectrum of the m = 1 sample shows a very slow increase up to around 0.4 eV, where a steep rise is observed which likely corresponds to the optical band gap Eg with an estimated value of 0.43 eV. The featureless and nearly flat increase observed further suggests that this compound is a direct band gap semiconductor. In contrast, the spectra of the m = 2, 3 compounds show a maximum near 0.22 eV followed by a shallow increase up to about 0.4 eV which marks the onset of a faster rise in the absorption. The first absorption edge near 0.15 eV might be associated with interband transitions or with the oscillating electron plasma near the plasma frequency due to the heavily doped nature of these two compounds (see below). The second increase at higher energies is likely due to optical transitions across the band gap, yielding estimated values of 0.38 and 0.40 eV (for direct transitions) and 0.26 and 0.27 eV (for indirect transitions) for the m = 2, 3 compounds, respectively. While the difference observed between the spectra G


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Inorganic Chemistry

Figure 5. SEM images and corresponding X-ray elemental maps of the (a) m = 2 and (b) m = 3 compounds.

of the m = 1 and m = 2 compounds indicates that the addition of a Bi2Se3 layer modifies the electronic band structure of the former, the similar spectra and Eg values on going from m = 2 to m = 3 suggest a weaker influence of the third Bi2Se3 layer. In the present case, the slight difference observed between the two Eg values for m = 2, 3 is likely due to modifications of the electronic band structure by the addition of the third Bi2Se3 layer. The influence of the Burstein−Moss effect observed in heavily doped semiconductors,62,63 that is, a shift of the optical band gap toward higher energies with an increase in the carrier concentration, seems unlikely due to the very similar electron concentrations measured in these two compounds (see below). Should it be direct or indirect, the optical Eg values of these three compounds are in line with those determined for other narrow-band-gap Pb−Bi−Se compounds such as Pb7Bi4Se13 (0.29 eV) and Pb6Bi2Se9 (0.58 eV).25,26 Transport Properties. The temperature dependence of the electrical resistivity of the m = 2, 3 compounds is shown in Figure 7a. For the former, ρ increases with increasing temperature below 300 K, suggestive of a metallic behavior. The anisotropy between the parallel and perpendicular directions is significant for both compounds, with the values

Figure 6. Optical absorption spectra for Pb5Bi6Se14 (m = 1), Pb5Bi12Se23 (m = 2), and Pb5Bi18Se32 (m = 3) plotted as [F(R) × E]2 vs E = ℏω (that is, for direct transitions). The extrapolation of the solid black lines to zero provides an estimate of the optical band gap Eg.

Figure 7. Temperature dependences of the (a) electrical resistivity and (b) thermopower for Pb5Bi12Se23 (m = 2) and Pb5Bi18Se32 (m = 3). The data of the m = 1 compound38 have been added for comparison. The color-coded symbols are similar in both panels. The solid lines are guides to the eye. H


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Inorganic Chemistry

Figure 8. Temperature dependences of the (a) Hall coefficient RH and (b) Hall mobility μH for the m = 1−3 compounds. The color-coded symbols for the m = 2, 3 compounds are similar in both panels. The data of the m = 1 compound,38 shown in green, have been added for comparison. The solid lines are guides to the eye.

Figure 9. (a) Total thermal conductivity κ as a function of temperature for Pb5Bi12Se23 (m = 2) and Pb5Bi18Se32 (m = 3). (b) Temperature dependence of the lattice thermal conductivity κL for the m = 2, 3 compounds. For comparison, the data of the m = 1 compound38 have been added. The solid lines are guides to the eye. The horizontal solid black line denotes the minimum thermal conductivity calculated from the experimental sound velocities.

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charge carrier mobility with an increase in the structural complexity of the unit cell. This result suggests that the number of interfaces between the Pb−Se and Bi−Se layers is a critical parameter. As we shall see below, a similar trend is observed for the lattice thermal conductivity. The total thermal conductivities κ of the m = 2, 3 samples are shown in Figure 9a. The data measured on the m = 1 compound are added for comparison. With no exception, these compounds exhibit glasslike thermal transport marked by the absence of an Umklapp maximum at low temperatures and very low κ values in the parallel direction in the whole temperature range. For the m = 2, 3 compounds, the κ values are similar at 300 K (∼0.7 W m−1 K−1) and slightly decrease upon warming to reach ∼0.6 W m−1 K−1 at 723 K. The strong anisotropy observed in the ρ values is reversed and is of comparable magnitude, with the values measured parallel to the pressing direction roughly twice as low as those measured perpendicular to the pressing direction. The significantly higher values observed in the perpendicular direction for these two compounds reflect their lower electrical resistivity, which gives rise to higher electronic contributions to the thermal conductivity. In order to unveil the trend in the lattice thermal conductivity with m, the electronic contribution has been estimated from the Wiedemann−Franz law κe = LT/ρ, where L is the Lorenz number. The temperature dependence of L was determined using a single parabolic band model as a first approximation. The calculated values vary from 2.45 × 10−8 V2 K−2 at low temperatures for both compounds down to 1.90 × 10−8 and 1.85 × 10−8 V2 K−2 at 723 K in the m = 3, 2 compounds, respectively. The lattice thermal conductivity κL = κ − κe is very low, approaching 0.5 W m−1 K−1 at 723 K, and is only weakly temperature dependent (Figure 9b). The κL values have been compared to the minimum thermal conductivity κmin estimated using the transverse vT and longitudinal vL sound velocities, determined to be 1144 and 1191 m s−1 and 2637 and 2382 m s−1 for the m = 2, 3 compounds, respectively.37,65 At high temperatures, κL is close to κmin ≈ 0.30 W m−1 K−1, indicating only little room for further lowering κL. As seen in the μH data, κL increases with increasing m in both directions despite an increase in the structural complexity of the unit cell. This variation does not follow the simple and general relationship between κL and the volume of the unit cell V observed in several thermoelectric compounds, for which κL values roughly scale as V−1.66 This unusual trend is further evidence showing that the number of Pb−Se/Bi−Se interfaces plays an important role in efficiently scattering acoustic phonons. These data overall imply that further increasing m beyond 3 would most probably result in a further increase in κL values, and in the limit of m → ∞, one would expect κL (and probably μH) to tend to the values of the binary Bi2Se3. The role of the number of interlayer interfaces and the presence of misalignment of lattice planes at these interfaces on κL has been also underlined in the Pb7Bi4Se13 and Pb6Bi2Se9 compounds.25,26 In the latter, the κL values show a 4-fold increase despite the presence of similar types of alternating layers in both structures.25,26 In addition to the number of Pb−Se/Bi−Se interfaces, several other ingredients may contribute to efficiently scatter acoustic phonons, resulting in the low κL values measured in the m = 1 compound. First, the large number of atoms per unit cell results in a large number of optical modes that limit the available phase space for acoustic phonons and give rise to

measured along the pressing direction being twice as high as those measured perpendicularly. This property indicates that the polycrystalline samples are textured after the SPS process due to the anisotropic crystal structure of these compounds and the strong anisotropy of the electrical properties measured in single crystals.39 Above 300 K, ρ(T) tends to saturate and varies only weakly upon further warming to 723 K. The overall complex behavior of the high-temperature part of ρ(T), similar to that observed in the m = 1 compound,37,38 is no longer visible in the m = 3 sample, which features significantly lower ρ values. The nearly linear increase in the whole temperature range indicates a more pronounced metallic character with respect to the m = 1, 2 compounds. The general trend observed in the electrical resistivity is confirmed by the temperature dependence of the thermopower (Figure 7b). For both compounds, the α values are isotropic to within experimental uncertainty. As in the m = 1 compound, these two compounds show negative α values, suggesting that electrons are the dominant charge carriers. Below 300 K, α increases linearly with temperature up to approximately −30 μV K−1 for both compounds. At higher temperatures, the measured values slightly differ with maximum values (in absolute values) of −130 and −100 μV K−1 achieved at 723 K for m = 2, 3, respectively. Both the n-type nature of the transport and the increase in the metallic character on going from m = 1 to m = 3 are consistent with Hall effect measurements carried out below 300 K (Figure 8a). The negative Hall coefficients RH are in agreement with the sign of the thermopower and are nearly temperature independent, indicating that both compounds can be viewed as heavily doped semiconductors. The n-type heavily doped nature of these two compounds has been attributed to the presence of Bi atoms on the Pb sites, which would act as donors assuming Pb2+, Bi3+, and Se2− valence states.45 The increase in the electron concentration on going from m = 1 to m = 2 is thus possibly related to a concomitant increase in the concentration of Bi atoms occupying the Pb positions. The Hall coefficient is not further influenced by the addition of a third Bi−Se layer, suggesting that the possible mixed Pb/Bi occupation is similar in the m = 2, 3 compounds. Within a single-carrier type model, the room-temperature RH values correspond to electron densities nH of 2.9 × 1020 and 2.8 × 1020 cm−3 for m = 2, 3, respectively. We note that these two values should be taken with some caution due to the strongly anisotropic crystal structures of these compounds, which gives rise to galvanomagnetic properties described by a tensor with up to five independent components.64 The anisotropy in the RH values is nevertheless limited in the present case (see Figure 8a), indicating that the aforementioned values can be considered as reasonable estimates of the actual electron concentrations. The temperature dependence of the Hall mobility μH is shown in Figure 8b. As expected from the layered crystal structure of these compounds, the μH values measured in the parallel direction are significantly lower than those in the perpendicular direction. The μH(T) curves are similar for both compounds and suggestive of electrons scattered by neutral impurities below ∼50 K. With increasing temperature, the μH values tend to decrease, indicating that acoustic phonon scattering becomes dominant above 100 K. What is more surprising, however, is the μH values that increase with increasing m in the perpendicular direction. This trend seems to be at odds with the general expectation of a decrease in J


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cally lower the thermal transport and impede charge carrier mobility. Rather, these data underline the essential role played by the number of Pb−Se/Bi−Se interfaces in determining both the electron and phonon transports. These results indicate that their thermoelectric performances might be improved by aliovalent substitutions to drive these compounds closer to a semiconducting state. Furthermore, the possible deviations from the ideal stoichiometry suggested by our chemical analyses require further experimental studies to better understand the complex chemistry of these interesting phases.

enhanced Umklapp scattering. The large thermal displacement parameters of the Pb atoms are indeed likely associated with low-energy optical modes as observed, for instance, in clathrates or in tetrahedrites.11−13,67−69 Second, the presence of stereochemically active lone-pair electrons of Pb and Bi likely responsible for the distortion of their octahedral environment might contribute to lowering the thermal transport, as recently proposed in the ternaries Pb7Bi4Se13 and Pb6Bi2Se9 and in several minerals such as tetrahedrites and CuSbS2.25,26,67−71 Finally, the possible presence of numerous nanoscale interfaces and stacking faults in polycrystalline specimens, which potentially act as additional phonon scatterers, as observed for instance in K2Bi8Se13,56 may also play a significant role in impeding heat transport. The dimensionless thermoelectric figure of merit ZT is shown in Figure 10 as a function of temperature for the m = 2,

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02656. SEM image of as-grown single-crystals of the m = 1 compound, crystallographic parameters of the m = 1, 2 compounds, Bi−Se interatomic distances for the m = 1− 3 compounds, annular bright-field images collected on single crystals of the m = 1−3 compounds, and optical spectra of the m = 1−3 compounds assuming indirect transitions (PDF) Accession Codes

CCDC 1582534−1582535 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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Figure 10. Temperature dependence of the dimensionless thermoelectric figure of merit ZT for the m = 1−3 compounds. The data of the m = 1 compound have been taken from ref 38. The solid lines are guides to the eye.

AUTHOR INFORMATION

Corresponding Author

*E-mail for B.L.: [email protected]. ORCID

Christophe Candolfi: 0000-0002-1248-5354 Notes

3 compounds. Similar peak ZT values of 0.25 and 0.20 are achieved at 723 K in the m = 2, 3 compounds, respectively. These values are lower than that obtained in the m = 1 compound (0.5 at 723 K37,38) due to the more pronounced metallic character of these two compounds.

The authors declare no competing financial interest.

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REFERENCES

(1) Goldsmid, H. J. In Thermoelectric Refrigeration; Springer: New York, 1964. (2) Thermoelectrics and its Energy Harvesting; Rowe, D. M., Ed.; CRC Press: Boca Raton, FL, 2012. (3) Bell, L. Cooling, Heating, Generating Power, and Recovering Waste Heat with Thermoelectric Systems. Science 2008, 321, 1457− 1461. (4) Slack, G. A. In CRC Handbook of Thermoelectrics; Rowe, M., Ed.; CRC Press: Boca Raton, FL, 1995. (5) Chen, Z.-G.; Han, G.; Cheng, L.; Zou, L. Nanostructured thermoelectric materials: Current research and future challenge. Prog. Nat. Sci. 2012, 22, 535−549. (6) Brown, S. R.; Kauzlarich, S. M.; Gascoin, F.; Snyder, G. J. Yb14MnSb11: New High Efficiency Thermoelectric Material for Power Generation. Chem. Mater. 2006, 18, 1873−1877. (7) Bux, S. K.; Zevalkink, A.; Janka, O.; Uhl, D.; Kauzlarich, S. M.; Snyder, G. J.; Fleurial, J.-P. Glass-like Lattice Thermal Conductivity and High Thermoelectric Efficiency in Yb9Mn4.2Sb9. J. Mater. Chem. A 2014, 2, 215−220. (8) Aydemir, U.; Zevalkink, A.; Ormeci, A.; Gibbs, Z. M.; Bux, S.; Snyder, G. J. Thermoelectric Enhancement in BaGa2Sb2 by Zn Doping. Chem. Mater. 2015, 27, 1622−1630.

SUMMARY AND CONCLUSION We report on a detailed characterization of the crystal structure and transport properties of the Pb5Bi12Se23 and Pb5Bi18Se32 compounds, which belong to the homologous series (PbSe)5(Bi2Se3)3m with m = 2, 3. The crystal structure of these compounds, investigated using a combination of singlecrystal X-ray diffraction data and high-resolution transmission electron microscopy, consists of alternating Pb−Se and m Bi− Se layers described in the monoclinic space groups C2/m (m = 2) and P21/m (m = 3). In contrast to the m = 1 compound, which shows a more semiconducting character, the m = 2, 3 compounds behave as degenerate narrow-band-gap n-type semiconductors, possibly due to mixed occupation of Bi and Pb on some sites of the crystal structure. The complex, lowsymmetry crystal structure of these compounds results in very low lattice thermal conductivity (0.5 W m−1 K−1 at 723 K). A comparison of the κL and μH values in this series indicates that increasing the complexity of the unit cell does not systematiK


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Inorganic Chemistry

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Crystal Structure and Transport Properties of the Homologous

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